Using mathematical concepts to describe physical phenomena lies at the heart of physics. Literature however shows that combining physics and mathematics is challenging for students on all levels and therefore, the study of students’ ways to link both fields is a hot topic in Physics Education Research. In the process of mathematization graphs have a fundamental role not only in the context of scientific communication but also within the process of gaining knowledge. But there is evidence of serious difficulties of students in reading, understanding and constructing graphs. Therefore we bring together different approaches, employing mainly qualitative research methods, to understand how students deal with graphs related to the interplay of mathematics and physics, how the reasoning differs between mathematical and physical problems and how students connect graphical and algebraic representations to physical concepts. Especially we describe in detail - in different areas of physics - which difficulties with graphs students of secondary school experience and which strategies they employ. For this purpose we analyse the activities of 8th grade students in graphing, we study the learning of 9th grade students in an interdisciplinary teaching-learning sequence and we describe the development of physicalmathematical concepts through the use of graphs, generated with on-line sensors
